Beta ensemble is one of the fundamental object in random matrix theory, describing the Gibbs measure of 1dim $N$ particles under the log potential at inverse temperature $beta$. High temperature limit refers to consider $beta to 0$ limit such that $N beta = c$. By changing $c$, it is expected to interpolate between the classical ($c=0$) and free ($c=infty$) probability theory. In this talk, I will review them and mention our recent results on Markov Klein transform and finite free convolutions. This is a joint work with Khanh Duy Trinh, Dung Hoang Trinh, and Ziteng Wang

https://indico.math.cnrs.fr/event/16565/